120000=112(1102)(x/1000)^2 eching

$$120000 = 112 ( 1102 ) ( \frac { x } { 1000 } ) ^ { 2 }$$

x uchun yechish

$$x = \frac{25000 \sqrt{23142}}{3857} \approx 986,031557196$$

$$x = -\frac{25000 \sqrt{23142}}{3857} \approx -986,031557196$$

Kvadrat ildizini topish bo'yicha qadamlar

123424 hosil qilish uchun 112 va 1102 ni ko'paytirish.

$$120000=123424\times \left(\frac{x}{1000}\right)^{2}$$

\frac{x}{1000}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$120000=123424\times \frac{x^{2}}{1000^{2}}$$

123424\times \frac{x^{2}}{1000^{2}} ni yagona kasrga aylantiring.

$$120000=\frac{123424x^{2}}{1000^{2}}$$

2 daraja ko‘rsatkichini 1000 ga hisoblang va 1000000 ni qiymatni oling.

$$120000=\frac{123424x^{2}}{1000000}$$

\frac{3857}{31250}x^{2} ni olish uchun 123424x^{2} ni 1000000 ga bo‘ling.

$$120000=\frac{3857}{31250}x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{3857}{31250}x^{2}=120000$$

Ikki tarafini \frac{31250}{3857} va teskari kasri \frac{3857}{31250} ga ko‘paytiring.

$$x^{2}=120000\times \frac{31250}{3857}$$

\frac{3750000000}{3857} hosil qilish uchun 120000 va \frac{31250}{3857} ni ko'paytirish.

$$x^{2}=\frac{3750000000}{3857}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{25000\sqrt{23142}}{3857} x=-\frac{25000\sqrt{23142}}{3857}$$

Kvadrat tenglamalaridan foydalanish qoidalari

123424 hosil qilish uchun 112 va 1102 ni ko'paytirish.

$$120000=123424\times \left(\frac{x}{1000}\right)^{2}$$

\frac{x}{1000}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$120000=123424\times \frac{x^{2}}{1000^{2}}$$

123424\times \frac{x^{2}}{1000^{2}} ni yagona kasrga aylantiring.

$$120000=\frac{123424x^{2}}{1000^{2}}$$

2 daraja ko‘rsatkichini 1000 ga hisoblang va 1000000 ni qiymatni oling.

$$120000=\frac{123424x^{2}}{1000000}$$

\frac{3857}{31250}x^{2} ni olish uchun 123424x^{2} ni 1000000 ga bo‘ling.

$$120000=\frac{3857}{31250}x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{3857}{31250}x^{2}=120000$$

Ikkala tarafdan 120000 ni ayirish.

$$\frac{3857}{31250}x^{2}-120000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{3857}{31250} ni a, 0 ni b va -120000 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3857}{31250}\left(-120000\right)}}{2\times \frac{3857}{31250}}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times \frac{3857}{31250}\left(-120000\right)}}{2\times \frac{3857}{31250}}$$

-4 ni \frac{3857}{31250} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-\frac{7714}{15625}\left(-120000\right)}}{2\times \frac{3857}{31250}}$$

-\frac{7714}{15625} ni -120000 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{\frac{1481088}{25}}}{2\times \frac{3857}{31250}}$$

\frac{1481088}{25} ning kvadrat ildizini chiqarish.

$$x=\frac{0±\frac{8\sqrt{23142}}{5}}{2\times \frac{3857}{31250}}$$

2 ni \frac{3857}{31250} marotabaga ko'paytirish.

$$x=\frac{0±\frac{8\sqrt{23142}}{5}}{\frac{3857}{15625}}$$

x=\frac{0±\frac{8\sqrt{23142}}{5}}{\frac{3857}{15625}} tenglamasini yeching, bunda ± musbat.

$$x=\frac{25000\sqrt{23142}}{3857}$$

x=\frac{0±\frac{8\sqrt{23142}}{5}}{\frac{3857}{15625}} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{25000\sqrt{23142}}{3857}$$

Tenglama yechildi.

$$x=\frac{25000\sqrt{23142}}{3857} x=-\frac{25000\sqrt{23142}}{3857}$$